It really depends on your usage and which apps you have running in the background. But my usage can vary from 4 to 6 hours on a good day (for instance only streaming video or constantly playing a light game or reading an e-book), but on days where too much stuff is going on and I keep turning the screen on and off repeatedly or take notes with the S-Pen, it can go down to 3.5h. Overall battery,though, still lets me go through a full day at least.

Read The Care and Feeding of Lithium Polymer Batteries first. Then, as SpookDroid said, the amount of screen on time depends on how long you have your screen on. It's like asking if 15,000 miles is the normal mileage for a car after 1 year. If that's how far you drive, yes. If you keep your screen on for 4 hours a day, 4 hours of screen on time per day is normal - for your usage. Some people might get 6 hours of screen a day, some may use it for 15 minutes.